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A239195 Sum of the next to smallest parts in the partitions of 4n into 4 parts with smallest part = 1. 1
1, 5, 17, 42, 78, 134, 215, 315, 447, 616, 812, 1052, 1341, 1665, 2045, 2486, 2970, 3522, 4147, 4823, 5579, 6420, 7320, 8312, 9401, 10557, 11817, 13186, 14630, 16190, 17871, 19635, 21527, 23552, 25668, 27924, 30325, 32825, 35477, 38286, 41202, 44282, 47531 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for sequences related to partitions

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

FORMULA

G.f.: x*(4*x^5+5*x^4+11*x^3+8*x^2+3*x+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Mar 12 2014

EXAMPLE

For a(n) add the numbers in the third columns.

                                               13+ 1 + 1 + 1

                                               12+ 2 + 1 + 1

                                               11+ 3 + 1 + 1

                                               10+ 4 + 1 + 1

                                               9 + 5 + 1 + 1

                                               8 + 6 + 1 + 1

                                               7 + 7 + 1 + 1

                                               11+ 2 + 2 + 1

                                               10+ 3 + 2 + 1

                              9 + 1 + 1 + 1    9 + 4 + 2 + 1

                              8 + 2 + 1 + 1    8 + 5 + 2 + 1

                              7 + 3 + 1 + 1    7 + 6 + 2 + 1

                              6 + 4 + 1 + 1    9 + 3 + 3 + 1

                              5 + 5 + 1 + 1    8 + 4 + 3 + 1

                              7 + 2 + 2 + 1    7 + 5 + 3 + 1

               5 + 1 + 1 + 1  6 + 3 + 2 + 1    6 + 6 + 3 + 1

               4 + 2 + 1 + 1  5 + 4 + 2 + 1    7 + 4 + 4 + 1

               3 + 3 + 1 + 1  5 + 3 + 3 + 1    6 + 5 + 4 + 1

1 + 1 + 1 + 1  3 + 2 + 2 + 1  4 + 4 + 3 + 1    5 + 5 + 5 + 1

    4(1)            4(2)           4(3)            4(4)       ..   4n

------------------------------------------------------------------------

     1               5              17              42        ..   a(n)

MATHEMATICA

b[n_] := Sum[(((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i) + (i + 2) (Floor[(4 n - 2 - i)/2] - i)) - ((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i)) - ((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i) + (i + 2) (Floor[(4 n - 2 - i)/2] - i))/(4 n)) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[b[n], {n, 50}]

PROG

(PARI) Vec(x*(4*x^5+5*x^4+11*x^3+8*x^2+3*x+1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Sep 22 2014

CROSSREFS

Cf. A238328, A238340, A238702, A238705, A238706, A239056, A239057, A239059, A239186.

Sequence in context: A122035 A052350 A318826 * A111746 A088645 A055609

Adjacent sequences:  A239192 A239193 A239194 * A239196 A239197 A239198

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Mar 11 2014

STATUS

approved

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Last modified February 28 00:28 EST 2020. Contains 332319 sequences. (Running on oeis4.)